Electric-field-mediated instability modes and Fréedericksz transition of thin nematic films

Abstract

Instabilities at the deformable free surface of a thin nematic liquid crystal film can develop interesting patterns when exposed to an external electrostatic field. A general linear stability analysis is performed involving the Ericksen–Leslie governing equations for the dynamics of the nematic film coupled with the anisotropic Maxwell stresses for the electric field to uncover the salient features of these instabilities. The study reveals the coexistence of twin instability modes: (i) long-wave interfacial mode – stimulated when the sole destabilizing influence of the electric field overcomes the Frank bulk elasticity and surface tension force, and (ii) finite-wavenumber mode – engendered by the combined destabilizing influence originating from the anisotropic electric field and Ericksen stress, for the films with positive dielectric anisotropy and weaker Frank bulk elasticity. The results reported here are in contrast with the same obtained from the more frequently employed long-wave approach. The air-to-liquid-crystal filling ratio between the electrodes as well as thermodynamic parameters such as the dielectric anisotropy, Frank elasticity, and director orientations across the film and boundaries are found to play crucial roles in the selection of modes, whereas kinetic parameters such as Leslie viscosity coefficients influence only the time scale of instability. Importantly, at higher field intensities a symmetry-breaking Fréedericksz-type transition of director orientations is found to happen, which also causes the transition of the dominant mode of instability from the long-wave to the finite-wavenumber mode for films with relatively lower values of Frank bulk elasticity and positive dielectric anisotropy.